A control point interpolation method for the non-parametric quantification of cerebral haemodynamics from dynamic susceptibility contrast MRI

Evaluation of parameters extracted from tissue residue functions in dynamic susceptibility contrast MRI: Healthy volunteers examined during normal breathing and spontaneous hyperventilation

Dynamic susceptibility contrast magnetic resonance imaging (DSC-MRI) is the most common MRI method in clinical environments for assessment of perfusion-related parameters. In this study, special emphasis was placed on the shape of the tissue residue function under different physiological conditions. DSC-MRI-based parameters assumed to reflect arterial delay and cerebral oxygen extraction were obtained by deconvolution of tissue and arterial contrast-agent concentration time curves. The established mean transit time (MTT) estimate was supplemented by biophysical modelling for extraction of the oxygen extraction capacity, quantified in terms of an apparent oxygen extraction fraction (AOEF) index. Eight healthy volunteers were examined during normal breathing and spontaneous hyperventilation. Whole-brain MTT and AOEF increased during hyperventilation in all volunteers (average increase 33 % and 30 %, respectively). The arterial delay, reflecting the inverse of arterial flow rate, was also prolonged in all volunteers, and the mean arterial delay was 63 % longer during hyperventilation. The corresponding whole-brain MTT estimates were 3.8 ± 0.7 s during normal breathing and 5.0 ± 1.3 s during hyperventilation (mean ± SD, n = 8). The applied Bézier curve deconvolution algorithm returned tissue residue functions of plausible shapes, i.e., without oscillations and negative values, and some indications that curve shape is relevant for improved assessment of oxygen extraction properties were demonstrated.

Effects of bolus injection duration on perfusion estimates in dynamic CT and dynamic susceptibility contrast MRI

Estimates of cerebral blood flow (CBF) and tissue mean transit time (MTT) have been shown to differ between dynamic CT perfusion (CTP) and dynamic susceptibility contrast MRI (DSC-MRI). This study investigates whether these discrepancies regarding CBF and MTT between CTP and DSC-MRI can be attributed to the different injection durations of these techniques. Five subjects were scanned using CTP and DSC-MRI. Region-wise estimates of CBF, MTT, and cerebral blood volume (CBV) were derived based on oscillatory index regularized singular value decomposition. A parametric model that reproduced the shape of measured time curves and characteristics of resulting perfusion parameter estimates was developed and used to simulate data with injection durations typical for CTP and DSC-MRI for a clinically relevant set of perfusion scenarios and noise levels. In simulations, estimates of CBF/MTT showed larger negative/positive bias and increasing variability for CTP when compared to DSC-MRI, especially for high CBF levels. While noise also affected estimates, at clinically relevant levels, the injection duration effect was larger. There are several methodological differences between CTP and DSC-MRI. The results of this study suggest that the injection duration is among those that can explain differences in estimates of CBF and MTT between these bolus tracking techniques.

Test-retest analysis of cerebral oxygen extraction estimates in healthy volunteers: comparison of methods based on quantitative susceptibility mapping and dynamic susceptibility contrast magnetic resonance imaging

Background

Estimation of the oxygen extraction fraction (OEF) by quantitative susceptibility mapping (QSM) magnetic resonance imaging (MRI) is promising but requires systematic evaluation. Extraction of OEF-related information from the tissue residue function in dynamic susceptibility contrast MRI (DSC-MRI) has also been proposed. In this study, whole-brain OEF repeatability was investigated, as well as the relationships between QSM-based OEF and DSC-MRI-based parameters, i.e., mean transit time (MTT) and an oxygen extraction index, referred to as apparent OEF (AOEF).

Method

Test-retest data were obtained from 20 healthy volunteers at 3 T. QSM maps were reconstructed from 3D gradient-echo MRI phase data, using morphology-enabled dipole inversion. DSC-MRI was accomplished using gradient-echo MRI at a temporal resolution of 1.24 s.

Results

The whole-brain QSM-based OEF was (40.4±4.8) % and, in combination with a previously published cerebral blood flow (CBF) estimate, this corresponds to a cerebral metabolic rate of oxygen level of CMRO2 = 3.36 ml O2/min/100 g. The intra-class correlation coefficient [ICC(2,1)] for OEF test-retest data was 0.73. The MTT-versus-OEF and AOEF-versus-OEF relationships showed correlation coefficients of 0.61 (p = 0.004) and 0.52 (p = 0.019), respectively.

Discussion

QSM-based OEF showed a convincing absolute level and good test-retest results in terms of the ICC. Moderate to good correlations between QSM-based OEF and DSC-MRI-based parameters were observed. The present results constitute an indicator of the level of robustness that can be achieved without applying extraordinary resources in terms of MRI equipment, imaging protocol, QSM reconstruction, and OEF analysis.

Quantitative Analysis of DCE and DSC-MRI: From Kinetic Modeling to Deep Learning

BACKGROUND

 Perfusion MRI is a well-established imaging modality with a multitude of applications in oncological and cardiovascular imaging. Clinically used processing methods, while stable and robust, have remained largely unchanged in recent years. Despite promising results from novel methods, their relatively minimal improvement compared to established methods did not generally warrant significant changes to clinical perfusion processing.

RESULTS AND CONCLUSION

 Machine learning in general and deep learning in particular, which are currently revolutionizing computer-aided diagnosis, may carry the potential to change this situation and truly capture the potential of perfusion imaging. Recent advances in the training of recurrent neural networks make it possible to predict and classify time series data with high accuracy. Combining physics-based tissue models and deep learning, using either physics-informed neural networks or universal differential equations, simplifies the training process and increases the interpretability of the resulting models. Due to their versatility, these methods will potentially be useful in bridging the gap between microvascular architecture and perfusion parameters, akin to MR fingerprinting in structural MR imaging. Still, further research is urgently needed before these methods may be used in clinical practice.

KEY POINTS

· Machine learning offers promising methods for processing of perfusion data.. · Recurrent neural networks can classify time series with high accuracy.. · Data augmentation is essentially especially when using small datasets..

CITATION FORMAT

· Rotkopf LT, Zhang KS, Tavakoli AA et al. Quantitative Analysis of DCE and DSC-MRI: From Kinetic Modeling to Deep Learning. Fortschr Röntgenstr 2022; DOI: 10.1055/a-1762-5854.

Non-parametric deconvolution using Bézier curves for quantification of cerebral perfusion in dynamic susceptibility contrast MRI

Objective

Deconvolution is an ill-posed inverse problem that tends to yield non-physiological residue functions R(t) in dynamic susceptibility contrast magnetic resonance imaging (DSC-MRI). In this study, the use of Bézier curves is proposed for obtaining physiologically reasonable residue functions in perfusion MRI.

Materials and methods

Cubic Bézier curves were employed, ensuring R(0) = 1, bounded-input, bounded-output stability and a non-negative monotonically decreasing solution, resulting in 5 parameters to be optimized. Bézier deconvolution (BzD), implemented in a Bayesian framework, was tested by simulation under realistic conditions, including effects of arterial delay and dispersion. BzD was also applied to DSC-MRI data from a healthy volunteer.

Results

Bézier deconvolution showed robustness to different underlying residue function shapes. Accurate perfusion estimates were observed, except for boxcar residue functions at low signal-to-noise ratio. BzD involving corrections for delay, dispersion, and delay with dispersion generally returned accurate results, except for some degree of cerebral blood flow (CBF) overestimation at low levels of each effect. Maps of mean transit time and delay were markedly different between BzD and block-circulant singular value decomposition (oSVD) deconvolution.

Discussion

A novel DSC-MRI deconvolution method based on Bézier curves was implemented and evaluated. BzD produced physiologically plausible impulse response, without spurious oscillations, with generally less CBF underestimation than oSVD.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10334-021-00995-0.

Stable spline deconvolution for dynamic susceptibility contrast MRI

PURPOSE

To present the stable spline (SS) deconvolution method for the quantification of the cerebral blood flow (CBF) from dynamic susceptibility contrast MRI.

METHODS

The SS method was compared with both the block-circulant singular value decomposition (oSVD) and nonlinear stochastic regularization (NSR) methods. oSVD is one of the most popular deconvolution methods in dynamic susceptibility contrast MRI (DSC-MRI). NSR is an alternative approach that we proposed previously. The three methods were compared using simulated data and two clinical data sets.

RESULTS

The SS method correctly reconstructed the dispersed residue function and its peak in presence of dispersion, regardless of the delay. In absence of dispersion, SS performs similarly to oSVD and does not correctly reconstruct the residue function and its peak. SS and NSR better differentiate healthy and pathologic CBF values compared with oSVD in all simulated conditions. Using acquired data, SS and NSR provide more clinically plausible and physiological estimates of the residue function and CBF maps compared with oSVD.

CONCLUSION

The SS method overcomes some of the limitations of oSVD, such as unphysiological estimates of the residue function and NSR, the latter of which is too computationally expensive to be applied to large data sets. Thus, the SS method is a valuable alternative for CBF quantification using DSC-MRI data. Magn Reson Med 78:1801-1811, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

Technical Pitfalls of Signal Truncation in Perfusion MRI of Glioblastoma

Dynamic susceptibility contrast (DSC) perfusion-weighted imaging (PWI) is widely used in clinical settings for the radiological diagnosis of brain tumor. The signal change in brain tissue in gradient echo-based DSC PWI is much higher than in spin echo-based DSC PWI. Due to its exquisite sensitivity, gradient echo-based sequence is the preferred method for imaging of all tumors except those near the base of the skull. However, high sensitivity also comes with a dynamic range problem. It is not unusual for blood volume to increase in gene-mediated cytotoxic immunotherapy-treated glioblastoma patients. The increase of fractional blood volume sometimes saturates the MRI signal during first-pass contrast bolus arrival and presents signal truncation artifacts of various degrees in the tumor when a significant amount of blood exists in the image pixels. It presents a hidden challenge in PWI, as this signal floor can be either close to noise level or just above and can go no lower. This signal truncation in the signal intensity time course is a significant issue that deserves attention in DSC PWI. In this paper, we demonstrate that relative cerebral blood volume and relative cerebral blood flow (rCBF) are underestimated due to signal truncation in DSC perfusion, in glioblastoma patients. We propose the use of second-pass tissue residue function in rCBF calculation using least-absolute-deviation deconvolution to avoid the underestimation problem.

Reliability of CT perfusion-derived CBF in relation to hemodynamic compromise in patients with cerebrovascular steno-occlusive disease: a comparative study with 15O PET

In the bolus tracking technique with computed tomography (CT) or magnetic resonance imaging, cerebral blood flow (CBF) is computed from deconvolution analysis, but its accuracy is unclear. To evaluate the reliability of CT perfusion (CTP)-derived CBF, we examined 27 patients with symptomatic or asymptomatic unilateral cerebrovascular steno-occlusive disease. Results from three deconvolution algorithms, standard singular value decomposition (sSVD), delay-corrected SVD (dSVD), and block-circulant SVD (cSVD), were compared with (15)O positron emission tomography (PET) as a reference standard. To investigate CBF errors associated with the deconvolution analysis, differences in lesion-to-normal CBF ratios between PET and CTP were correlated with prolongation of arterial-tissue delay (ATD) and mean transit time (MTT) in the lesion hemisphere. Computed tomography perfusion results strongly depended on the deconvolution algorithms used. Standard singular value decomposition showed ATD-dependent underestimation of CBF ratio, whereas cSVD showed overestimation of the CBF ratio when MTT was severely prolonged in the lesions. The computer simulations reproduced the trend observed in patients. Deconvolution by dSVD can provide lesion-to-normal CBF ratios less dependent on ATD and MTT, but requires accurate ATD maps in advance. A practical and accurate method for CTP is required to assess CBF in patients with MTT-prolonged regions.

Automatic determination of the arterial input function in dynamic susceptibility contrast MRI: comparison of different reproducible clustering algorithms

Introduction

Arterial input function (AIF) plays an important role in the quantification of cerebral hemodynamics. The purpose of this study was to select the best reproducible clustering method for AIF detection by comparing three algorithms reported previously in terms of detection accuracy and computational complexity.

Methods

First, three reproducible clustering methods, normalized cut (Ncut), hierarchy (HIER), and fast affine propagation (FastAP), were applied independently to simulated data which contained the true AIF. Next, a clinical verification was performed where 42 subjects participated in dynamic susceptibility contrast MRI (DSC-MRI) scanning. The manual AIF and AIFs based on the different algorithms were obtained. The performance of each algorithm was evaluated based on shape parameters of the estimated AIFs and the true or manual AIF. Moreover, the execution time of each algorithm was recorded to determine the algorithm that operated more rapidly in clinical practice.

Results

In terms of the detection accuracy, Ncut and HIER method produced similar AIF detection results, which were closer to the expected AIF and more accurate than those obtained using FastAP method; in terms of the computational efficiency, the Ncut method required the shortest execution time.

Conclusion

Ncut clustering appears promising because it facilitates the automatic and robust determination of AIF with high accuracy and efficiency.

Reliable estimation of capillary transit time distributions using DSC-MRI

The regional availability of oxygen in brain tissue is traditionally inferred from the magnitude of cerebral blood flow (CBF) and the concentration of oxygen in arterial blood. Measurements of CBF are therefore widely used in the localization of neuronal response to stimulation and in the evaluation of patients suspected of acute ischemic stroke or flow-limiting carotid stenosis. It was recently demonstrated that capillary transit time heterogeneity (CTH) limits maximum oxygen extraction fraction (OEF(max)) that can be achieved for a given CBF. Here we present a statistical approach for determining CTH, mean transit time (MTT), and CBF using dynamic susceptibility contrast magnetic resonance imaging (DSC-MRI). Using numerical simulations, we demonstrate that CTH, MTT, and OEF(max) can be estimated with low bias and variance across a wide range of microvascular flow patterns, even at modest signal-to-noise ratios. Mean transit time estimated by singular value decomposition (SVD) deconvolution, however, is confounded by CTH. The proposed technique readily identifies malperfused tissue in acute stroke patients and appears to highlight information not detected by the standard SVD technique. We speculate that this technique permits the non-invasive detection of tissue with impaired oxygen delivery in neurologic disorders such as acute ischemic stroke and Alzheimer's disease during routine diagnostic imaging.

Evaluating the feasibility of an agglomerative hierarchy clustering algorithm for the automatic detection of the arterial input function using DSC-MRI

During dynamic susceptibility contrast-magnetic resonance imaging (DSC-MRI), it has been demonstrated that the arterial input function (AIF) can be obtained using fuzzy c-means (FCM) and k-means clustering methods. However, due to the dependence on the initial centers of clusters, both clustering methods have poor reproducibility between the calculation and recalculation steps. To address this problem, the present study developed an alternative clustering technique based on the agglomerative hierarchy (AH) method for AIF determination. The performance of AH method was evaluated using simulated data and clinical data based on comparisons with the two previously demonstrated clustering-based methods in terms of the detection accuracy, calculation reproducibility, and computational complexity. The statistical analysis demonstrated that, at the cost of a significantly longer execution time, AH method obtained AIFs more in line with the expected AIF, and it was perfectly reproducible at different time points. In our opinion, the disadvantage of AH method in terms of the execution time can be alleviated by introducing a professional high-performance workstation. The findings of this study support the feasibility of using AH clustering method for detecting the AIF automatically.

Modeling and correction of bolus dispersion effects in dynamic susceptibility contrast MRI

PURPOSE

Bolus dispersion in DSC-MRI can lead to errors in cerebral blood flow (CBF) estimation by up to 70% when using singular value decomposition analysis. However, it might be possible to correct for dispersion using two alternative methods: the vascular model (VM) and control point interpolation (CPI). Additionally, these approaches potentially provide a means to quantify the microvascular residue function.

METHODS

VM and CPI were extended to correct for dispersion by means of a vascular transport function. Simulations were performed at multiple dispersion levels and an in vivo analysis was performed on a healthy subject and two patients with carotid atherosclerotic disease.

RESULTS

Simulations showed that methods that could not address dispersion tended to underestimate CBF (ratio in CBF estimation, CBFratio = 0.57-0.77) in the presence of dispersion; whereas modified CPI showed the best performance at low-to-medium dispersion; CBFratio = 0.99 and 0.81, respectively. The in vivo data showed trends in CBF estimation and residue function that were consistent with the predictions from simulations.

CONCLUSION

In patients with atherosclerotic disease the estimated residue function showed considerable differences in the ipsilateral hemisphere. These differences could partly be attributed to dispersive effects arising from the stenosis when dispersion corrected CPI was used. It is thus beneficial to correct for dispersion in perfusion analysis using this method.

A generalized mathematical framework for estimating the residue function for arbitrary vascular networks

The microvasculature plays a vital part in the cardiovascular system. Any impairment to its function can lead to significant pathophysiological effects, particularly in organs such as the brain where there is a very tight coupling between structure and function. However, it is extremely difficult to quantify the health of the microvasculature in vivo, other than by assessing perfusion, using techniques such as arterial spin labelling. Recent work has suggested that the flow distribution within a voxel could also be a valuable measure. This can also be measured clinically, but as yet has not been related to the properties of the microvasculature due to the difficulties in modelling and characterizing these strongly inter-connected networks. In this paper, we present a new technique for characterizing an existing physiologically accurate model of the cerebral microvasculature in terms of its residue function. A new analytical mathematical framework for calculation of the residue function, based on the mass transport equation, of any arbitrary network is presented together with results from simulations. We then present a method for characterizing this function, which can be directly related to clinical data, and show how the resulting parameters are affected under conditions of both reduced perfusion and reduced network density. It is found that the residue function parameters are affected in different ways by these two effects, opening up the possibility of using such parameters, when acquired from clinical data, to infer information about both the network properties and the perfusion distribution. These results open up the possibility of obtaining valuable clinical information about the health of the microvasculature in vivo, providing additional tools to clinicians working in cerebrovascular diseases, such as stroke and dementia.